Question

if fog(x)=((2x-1)/x) and g(x)=5x+2. find f(x)

Answer 1

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Answer:

  f(x) = (2x -9)/(x -2)

Step-by-step explanation:

We can use the fact that g(g^-1(x)) = x.

  $(f\circ g)(x) = f(g(x))\\\\(f\circ g)(g^{-1}(x))=f(g(g^{-1}(x)))=f(x)$

So, we need to know the inverse of g(x):

  x = g(y)

  x = 5y +2

  x -2 = 5y

  y = (x -2)/5 . . . . inverse of g(x)

Then we have ...

  $f(x)=(f\circ g)(g^{-1}(x))=(f\circ g)\left(\dfrac{x-2}{5}\right)\\\\f(x)=\dfrac{2\left(\dfrac{x-2}{5}\right)-1}{\left(\dfrac{x-2}{5}\right)}=\dfrac{2x-4-5}{x-2}\\\\\boxed{f(x)=\dfrac{2x-9}{x-2}}$